I don't know what you mean by PnC, and the Wikipedia disambiguation page didn't help: https://en.wikipedia.org/wiki/PNC

> It seems way more unreasonable to assert that, in fact, there is some consistent, complete ethical framework out there, but we havent found it yet, than it is to just accept that some kernels of truth or sense are not formalizable in the classical sense.

We can prove that complete and consistent set of axioms for all mathematics is impossible. An equivalent proof for ethics would itself be useful.

However, we do not need to concern ourselves with infinite sets etc. for ethics the way we do with natural numbers, as there's only relatively (in mathematical terms) small number of real people to interact with or influence the lives of.

We may not be able to reach an optimal outcome with even a limited n, if it turns out to be akin to P != NP. But even knowing that, would itself be useful.

The problem I have with Utilitarianism isn't any of these things, it's that it's simply trying to maximise how much utility there is in the world, then immediately tripping over itself because the terms "utility", "maximise" and "the world" aren't well-defined, and the way it is introduced is simply adding up.